Bounded Integer Solutions

How many integer solutions satisfy $x_{1} + x_{2} + x_{3} = 20$ with $x_{1} \geq 2$ , $x_{2} \geq 3$ , $x_{3} \geq 4$ ?

Quant interview-style problem · QS-C015

Your answer

Think first. Use hints deliberately. Study the reasoning only when you need it.